Simultaneous Equations

 

SIMULTANEOUS EQUATIONS:-



 Often, solving a problem requires an equation. Sometimes there is more than one unknown variable in an equation. 


For example:

3x + 6y = 15

Here, there can be multiple combinations of answers of x and y, and trial and error is not an efficient way of solving the equation. This is when other equations are given to help find the unknown variables algebrically. Let us take another equation and calculate 'simultaneously'.

2x - 2y = -4

Now let us write the equations together:

3x + 6y = 15______________equation 1

2x - 2y = -2_______________equation 2

Now, we multiply both the equations in such a way that the coefficient of one variable becomes equal:

6x + 12y = 30 we multiplied the first equation by 2.

6x - 6y = -6 we multiplied the second equation by 3.


The coeeficient of 'x' becomes 6 in both!

Now we can subtract the equations to get rid of the 'x'.

All we do in this step is change the sign of every corresponding variable:


(6x-6x) + (12y + 6y) = (30 + 6)

We changed the sign of the 6x, the -6y and the -6.


Now, we get the equation:

18y=36

Hence, 

y=2

Now we know y, so it is easy to find x by plugging in the value in any one equation. 

3x + 6(2)=15

3x = 15-12

3x=3

So, 

x=1

and y=2!


Instead of x and y, you might come across two different unknown variables, but the method always remains the same!

1. Multiply one/both the equations for one of the coefficients to be the same.

2. Subtract one equation from another

3. Solve for one of the variables

4. Subtitute that variable back in place to find the other solution!



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